M indian. If during the conceiving of first child parents were slim and during second child they were obese, more chance of second child becoming obese?

Yes, but: The risk has more to do with parents maintaining an "obese lifestyle." the interesting thing is, when obese children go to a weight reduction camp, come back slimmer and maintain healthy weight a year later, their parents are statistically more likely to lose weight as well, by being influenced by changes in the child's routine.